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Quadratic equation x2-k-x equals 0

Updated: 4/28/2022
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Brudogs

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14y ago

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Moriah Grady

Lvl 10
3y ago
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Wiki User

14y ago

The equation x^2-x-k=0 is the equation of a parabola. Let k=0 for example and we have x^2-x=0 or x(x-1)=0 This is a parabola with x intercepts at 0 and 1. The y intercept is 0 as well. Look at x^2-x-1=0 This does not factor over the integers but it does factor over the real numbers as (2x+Squareroot(5)-1)(2x-Squareroot(5)-1) so let each quantity in the product equal 0 and find the x intercepts of the parabola. In general ax^2+bx+c=0 is a quadratic equation if a is not 0. The graph of this equation is a parabola as can be easily proved. The quadratic you gave is a special case of this where b=-1 and c=-k

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